STRING EQUATIONS FOR THE KDV HIERARCHY AND THE GRASSMANNIAN

The Grassmannian model for the Korteweg-de Vries hierarchy is used to describe the translational, Galilean and scaling self-similar solution s of this hierarchy, These solutions are characterized by the string e quations appearing in two-dimensional quantum gravity. In particular, the subsets of the Sato Grassmannian corresponding to solutions of the string equations are found. The well known Adler-Moser rational solut ions are obtained as well as a three-parameter family of solutions ass ociated with the Painleve II equation.